Gordon Brown is expected to go to Washington next month or early in March to meet Barack Obama as he tries to refashion Britain's "special relationship" with the US after eight bruising years with George Bush.

Downing Street is telling the White House that the prime minister does not expect to be one of the first leaders to meet the new president.

Senior British government sources said yesterday that the Obama White House is following custom with the new president's first meetings; it means that Felipe Calderón, the president of Mexico, and Stephen Harper, the prime minister of Canada, will be first in the queue.

No 10 accepts that Brown might not even be the first EU leader through the door of the Oval Office. George Bush snr met Helmut Kohl, the then German chancellor, before seeing Margaret Thatcher in 1989, and his son met France's Jacques Chirac before Tony Blair in 2001.

Sir Nigel Sheinwald, the British ambassador to Washington, yesterday prepared the ground for Obama to meet President Nicolas Sarkozy, or Chancellor Angela Merkel in Washington before Brown.

"It is important to see it not in terms of a zero sum game. It actually strengthens the UK, and helps the UK-US relationship, if America does have good relations with France and Germany. It can only improve things if Europe as a whole is seen to be co-operating actively, both militarily but also economically, round the world in concert with the US," Sheinwald told BBC Radio 4's the World at One programme. He pointed out that Britain's focus was on the G20 summit in London on 2 April, to be chaired by Brown, which will be one of the new president's first overseas visits.

"The important thing for the UK is that, whatever happens, we will have President Obama in London at the beginning of April," he said of the summit. This will take place a day before Obama attends Nato's 60th anniversary summit, to be held jointly in France and Germany in the border towns of Strasbourg and Kehl.

Simon Macdonald, the prime minister's chief foreign policy adviser, is to travel to Washington to meet General Jim Jones, Obama's national security adviser, to discuss an early meeting with Brown and to prepare the ground for the G20 summit. Macdonald has already spoken to Jones.

Aides, who have held "under the radar" contacts since Obama's election victory in November, are confident that Brown will form a close relationship with Obama. They are careful not to draw parallels with Harold Macmillan, who regarded himself as a father figure to John Kennedy, 23 years his junior. Brown, who is 10 years older than Obama, believes that stance would be seen as patronising.

His first meeting with Obama, at the British embassy in Washington last April, went well. But it was limited because it had to be timed down to the second not to last longer than meetings Brown had with the two other presidential candidates, Hillary Clinton and John McCain.

Brown's most important meeting with Obama took place in Downing Street in July after Obama's address to hundreds of thousands of cheering supporters in Berlin. The two men met alone for 90 minutes and were joined by officials round the cabinet table afterwards.

As published authors, Brown and Obama are two of the most academic leaders on the world stage. Brown is also close to Larry Summers, head of the White House National Economic Council, who taught Ed Balls at Harvard University.